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A091512
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2^a(n) divides (2n)^n: exponent of 2 in (2n)^n.
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6
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1, 4, 3, 12, 5, 12, 7, 32, 9, 20, 11, 36, 13, 28, 15, 80, 17, 36, 19, 60, 21, 44, 23, 96, 25, 52, 27, 84, 29, 60, 31, 192, 33, 68, 35, 108, 37, 76, 39, 160, 41, 84, 43, 132, 45, 92, 47, 240, 49, 100, 51, 156, 53, 108, 55, 224, 57, 116, 59, 180, 61, 124, 63
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = A007814(A000312(n)) = n*A001511(n) = A069895(n)/2.
G.f.: sum(k>=0, 2^k*x^2^k/(1-x^2^k)^2).
Recurrence: a(0) = 0, a(2n) = 2a(n) + 2n, a(2n+1) = 2n+1.
Dirichlet g.f.: zeta(s-1)*2^s/(2^s-2). - Ralf Stephan, Jun 17 2007
Mobius transform of A162728, where x/(1-x)^2 = Sum_{n>=1} A162728(n)*x^n/(1+x^n). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 12 2009]
a(n) = A162728(2n)/phi(2n), where x/(1-x)^2 = Sum_{n>=1} A162728(n)*x^n/(1+x^n). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 12 2009]
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MATHEMATICA
| Table[ Part[ Flatten[ FactorInteger[2n^n]], 2], {n, 1, 124}]
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PROG
| (PARI) a(n)=n*(valuation(n, 2)+1)
(PARI) a(n)=if(n<1, 0, if(n%2==0, 2*a(n/2)+n, n))
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CROSSREFS
| Cf. A091519, A090740, A090739.
Cf. A162728. [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 12 2009]
Sequence in context: A204291 A099377 A121844 * A106285 A193800 A061727
Adjacent sequences: A091509 A091510 A091511 * A091513 A091514 A091515
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KEYWORD
| nonn,mult,easy
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AUTHOR
| R. Stephan (ralf(AT)ark.in-berlin.de) and Labos E. (labos(AT)ana.sote.hu), Jan 18 2004
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